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Outlier Detection
Chapter 12 of Data Mining: Concepts and Techniques
JIAWEI HAN, MICHELINE KAMBER, JIAN PEI
PRESENTED BY: SHERRY ZHU EECS6412 WINTER 2017
MARCH 15, 2017
OUTLIER DETECTION CHAPTER 12 OF DATA MINING: CONCEPTS AND TECHNIQUES
Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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What Are Outliers?
• Outlier: A data object that deviates significantly from the normal objects as if it were generated by a different mechanism
Ex.: Unusual credit card transaction
• Outliers ≠ Noise data • Outliers are interesting: It violates the mechanism that generates the normal data
• Outlier detection vs. novelty detection: early stage, outlier; but later merged into the model
• Applications:
Credit card fraud detection
Medical analysis
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Types of Outliers
Three kinds: global, contextual and collective outliers
Global outlier (or point anomaly)
◦ Object is Og if it significantly deviates from the rest of the data set
◦ Issue: Find an appropriate measurement of deviation
Contextual outlier (or conditional outlier)
◦ Object is Oc if it deviates significantly based on a selected context
◦ Attributes of data objects should be divided into two groups ◦ Contextual attributes: defines the context, e.g., time & location ◦ Behavioral attributes: characteristics of the object, used in outlier evaluation, e.g., temperature
◦ Can be viewed as a generalization of local outliers
◦ Issue: How to define or formulate meaningful context?
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Types of Outliers (Cont’d)
Collective Outliers
◦ A subset of data objects collectively deviate significantly from the whole data set, even if the individual data objects may not be outliers
◦ Applications: ◦ Detection of collective outliers
◦ Consider not only behavior of individual objects, but also that of groups of objects
◦ Need to have the background knowledge on the relationship among data objects, such as a distance or similarity measure on objects.
* A data set may have multiple types of outlier
* One object may belong to more than one type of outlier
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Challenges of Outlier Detection

Modeling normal objects and outliers properly

Application-specific outlier detection

Handling noise in outlier detection
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Understandability
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Outlier Detection Methods
Two ways to categorize outlier detection methods: ◦ Based on whether user‐labeled examples of outliers can be obtained: ◦ Supervised, semi‐supervised vs. unsupervised methods
◦ Based on assumptions about normal data and outliers:
◦ Statistical, proximity‐based, and clustering‐based methods
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Outlier Detection I: Supervised Methods
◦
Modeling outlier detection as a classification problem
◦ Samples examined by domain experts used for training & testing
◦ Methods for Learning a classifier for outlier detection effectively:
◦ Model normal objects & report those not matching the model as outliers, or
◦ Model outliers and treat those not matching the model as normal
◦ Challenges
◦ Imbalanced classes, i.e., outliers are rare: Boost the outlier class and make up some artificial outliers
◦ Catch as many outliers as possible, i.e., recall is more important than accuracy (i.e., not mislabeling normal objects as outliers)
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Outlier Detection II: Unsupervised Methods • Assume the normal objects are somewhat ``clustered'‘ into multiple groups, each having some distinct features
• An outlier is expected to be far away from any groups of normal objects
• Weakness: Cannot detect collective outlier effectively
‐ Normal objects may not share any strong patterns, but the collective outliers may share high similarity in a small area
‐ Unsupervised methods may have a high false positive rate but still miss many real outliers.
‐ Supervised methods can be more effective, e.g., identify attacking some key resources
• Many clustering methods can be adapted for unsupervised methods
‐ Procedure: Find clusters, then outliers  those not belonging to any cluster
‐ Problem 1: Hard to distinguish noise from outliers
‐ Problem 2: Costly since first clustering: but far less outliers than normal objects OUTLIER DETECTION CHAPTER 12 OF DATA MINING: CONCEPTS AND TECHNIQUES
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Outlier Detection III: Semi‐Supervised Methods
• Situation: In many applications, the number of labeled data is often small: Labels could be on outliers only, normal objects only, or both
• Semi‐supervised outlier detection thus is regarded as applications of semi‐supervised learning
• If some labeled normal objects are available
◦ Use the labeled examples and the proximate unlabeled objects to train a model for normal objects  those not fitting the model of normal objects are detected as outliers
• If only some labeled outliers are available, a small number of labeled outliers many not cover the possible outliers well
◦ To improve the quality of outlier detection, one can get help from models for normal objects learned from unsupervised methods OUTLIER DETECTION CHAPTER 12 OF DATA MINING: CONCEPTS AND TECHNIQUES
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Outlier Detection IV: Statistical Methods
• Statistical methods (also known as model‐based methods) assume that the normal data follow some statistical model (a stochastic model)
◦ The data not following the model are outliers.
• Example: First use Gaussian distribution to model the normal data (on bb)
◦ For each object y in region R, estimate gD(y), the probability of y fits the Gaussian distribution
◦ If gD(y) is very low, y is unlikely generated by the Gaussian model, thus an outlier
• Effectiveness of statistical methods: highly depends on whether the assumption of statistical model holds in the real data
• There are rich alternatives to use various statistical models
◦ E.g., parametric vs. non‐parametric
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Outlier Detection V: Proximity‐Based Methods
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An object is an outlier if the nearest neighbors of the object are far away, i.e., the proximity of the object is significantly deviated from the proximity of most of the other objects in the same data set
Example: Model the proximity of an object using its 3 nearest neighbors(on bb)
 Objects in region R are substantially different from other objects in the data set  R are outliers
The effectiveness of proximity‐based methods highly relies on the proximity measure.
In some applications, proximity or distance measures cannot be obtained easily. Often have a difficulty in finding a group of outliers which stay close to each other
Two major types of proximity‐based outlier detection
Distance‐based vs. density‐based
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Outlier Detection VI: Clustering‐Based Methods
• Normal data belong to large and dense clusters, whereas outliers belong to small or sparse clusters, or do not belong to any clusters
• Example: two clusters (on bb)
 All points not in R form a large cluster
 The two points in R form a tiny cluster, thus are outliers
• Since there are many clustering methods, there are many clustering‐based outlier detection methods as well
• Clustering is expensive: straightforward adaption of a clustering method for outlier detection can be costly and does not scale up well for large data sets
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Statistical Approaches
• Statistical approaches assume that the objects in a data set are generated by a stochastic process (idea)
• Methods are divided into two categories: parametric vs. non‐parametric
• Parametric method
◦ Assumes that the normal data is generated by a parametric distribution with parameter θ
◦ The probability density function of the parametric distribution f(x, θ) gives the probability that object x is generated by the distribution
◦ The smaller this value, the more likely x is an outlier
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Statistical Approaches Cont’d
• Non‐parametric method
◦ Not assume an a‐priori statistical model and determine the model from the input data
◦ Not completely parameter free but consider the number and nature of the parameters are flexible and not fixed in advance
◦ Examples: histogram and kernel density estimation
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Parametric Methods I: Detection Univariate Outliers Based on Normal Distribution
• Univariate data: A data set involving only one attribute or variable
• Often assume that data are generated from a normal distribution, learn the parameters from the input data, and identify the points with low probability as outliers
• Ex: Avg. temp.: {24.0, 28.9, 28.9, 29.0, 29.1, 29.1, 29.2, 29.2, 29.3, 29.4}
◦ Use the maximum likelihood method to estimate μ and σ
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Parametric Methods I: Detection Univariate Outliers Based on Normal Distribution Cont’d
Taking derivatives with respect to μ and σ2, we derive the
following maximum likelihood estimates
For the above data with n = 10, we have
Then (24 – 28.61) /1.51 = – 3.04 < –3, 24 is an outlier
since
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Parametric Methods I: The Grubb’s Test
• Univariate outlier detection: The Grubb's test (maximum normed residual test) ─ another statistical method under normal distribution ◦ For each object x in a data set, compute its z‐score: x is an outlier if where is the value taken by a t‐distribution at a significance level of α/(2N), and N is the # of objects in the data set
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Parametric Methods II: Detection of Multivariate Outliers
• Multivariate data: A data set involving two or more attributes or variables
• Transform the multivariate outlier detection task into a univariate outlier detection problem
• Method 1. Compute Mahalaobis distance
◦ Let ō be the mean vector for a multivariate data set. Mahalaobis distance for an object o to ō
is MDist(o, ō) = (o – ō )T S –1(o – ō) where S is the covariance matrix
◦ Use the Grubb's test on this measure to detect outliers
• Method 2. Use χ2 –statistic:
◦ where Ei is the mean of the i‐dimension among all objects, and n is the dimensionality
◦ If χ2 –statistic is large, then object oi is an outlier
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Parametric Methods III: Using Mixture of Parametric Distributions
• Assuming data generated by a normal distribution could be sometimes overly simplified
• Example: The objects between the two clusters cannot be captured as outliers since they are close to the estimated mean
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Parametric Methods III: Using Mixture of Parametric Distributions Cont’d

To overcome this problem, assume the normal data is generated by
two normal distributions. For any object o in the data set, the
probability that o is generated by the mixture of the two distributions
is given by
where fθ1 and fθ2 are the probability density functions of θ1 and θ2

Then use EM algorithm to learn the parameters μ1, σ1, μ2, σ2 from data

An object o is an outlier if it does not belong to any cluster
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Non‐Parametric Methods: Detection Using Histogram
• The model of normal data is learned from the input data without any a priori structure. • Often makes fewer assumptions about the data, and thus can be applicable in more scenarios
• Outlier detection using histogram:
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Non‐Parametric Methods: Detection Using Histogram Cont’d
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Problem: Hard to choose an appropriate bin size for histogram
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Too small bin size → normal objects in empty/rare bins, false
positive
Too big bin size → outliers in some frequent bins, false
negative
Solution: Adopt kernel density estimation to estimate the
probability density distribution of the data. If the estimated density
function is high, the object is likely normal. Otherwise, it is likely an
outlier.
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Proximity‐Based Approaches: Distance‐
Based vs. Density‐Based Outlier Detection
• Intuition: Objects that are far away from the others are outliers
• Assumption of proximity‐based approach: The proximity of an outlier deviates significantly from that of most of the others in the data set
• Two types of proximity‐based outlier detection methods
◦ Distance‐based outlier detection: An object o is an outlier if its neighborhood does not have enough other points
◦ Density‐based outlier detection: An object o is an outlier if its density is relatively much lower than that of its neighbors
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Clustering‐Based Outlier Detection (1 & 2):
Not belong to any cluster, or far from the closest one
• An object is an outlier if (1) it does not belong to any cluster, (2) there is a large distance between the object and its closest cluster , or (3) it belongs to a small or sparse cluster • Case I: Not belong to any cluster
◦ Identify animals not part of a flock: Using a density‐based clustering method such as DBSCAN
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Clustering‐Based Outlier Detection (1 & 2):
Not belong to any cluster, or far from the closest one Cont’d
• Case 2: Far from its closest cluster  Using k‐means, partition data points of into clusters  For each object o, assign an outlier score based on its distance from its closest center If dist(o, co)/avg_dist(co) is large, likely an outlier
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Clustering‐Based Outlier Detection (1 & 2):
Not belong to any cluster, or far from the closest one Cont’d
• Ex. Intrusion detection: Consider the similarity between data points and the clusters in a training data set
 Use a training set to find patterns of “normal” data, e.g., frequent itemsets in each segment, and cluster similar connections into groups
 Compare new data points with the clusters mined—
Outliers are possible attacks
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Clustering-Based Outlier Detection (3):
Detecting Outliers in Small Clusters
FindCBLOF: Detect outliers in small clusters
◦ Find clusters, and sort them in decreasing size
◦ To each data point, assign a cluster‐based local outlier factor (CBLOF):
◦ If obj p belongs to a large cluster, CBLOF = cluster_size X similarity between p and cluster
◦ If p belongs to a small one, CBLOF = cluster_size X similarity btw. p and the closest large cluster
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Clustering-Based Outlier Detection (3):
Detecting Outliers in Small Clusters Cont’d

Ex. In the figure, o is outlier since its closest large cluster is C1, but
the similarity between o and C1 is small. For any point in C3, its
closest large cluster is C2 but its similarity from C2 is low, plus |C3| = 3
is small
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Clustering‐Based Method: Strength and Weakness
Strength
1) Detect outliers without requiring any labeled data
2) Work for many types of data
3) Clusters can be regarded as summaries of the data
4) Once the cluster are obtained, need only compare any object against
the clusters to determine whether it is an outlier (fast)
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Clustering‐Based Method: Strength and Weakness Cont’d
Weakness
1) Effectiveness depends highly on the clustering method used—they may not be optimized for outlier detection
2) High computational cost: Need to first find clusters
3) A method to reduce the cost: Fixed‐width clustering
 A point is assigned to a cluster if the center of the cluster is within a pre‐defined distance threshold from the point
 If a point cannot be assigned to any existing cluster, a new cluster is created and the distance threshold may be learned from the training data under certain conditions
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Classification‐Based Method I: One‐Class Model
• Idea: Train a classification model that can distinguish “normal” data from outliers
• A brute‐force approach: Consider a training set that contains samples labeled as “normal” and others labeled as “outlier”
◦ But, the training set is typically heavily biased: # of “normal” samples likely far exceeds # of outlier samples
◦ Cannot detect unseen anomaly
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Classification‐Based Method I: One‐Class Model Cont’d

One-class model: A classifier is built to describe only the normal
class.
 Learn the decision boundary of the normal class using
classification methods such as SVM
 Any samples that do not belong to the normal class (not within
the decision boundary) are declared as outliers
 Adv: can detect new outliers that may not appear close to any
outlier objects in the training set
 Extension: Normal objects may belong to multiple classes
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Classification‐Based Method II: Semi‐Supervised Learning
• Semi‐supervised learning: Combining classification‐
based and clustering‐based methods
• Method
◦ Using a clustering‐based approach, find a large cluster, C, and a small cluster, C1
◦ Since some objects in C carry the label “normal”, treat all objects in C as normal
◦ Use the one‐class model of this cluster to identify normal objects in outlier detection
◦ Since some objects in cluster C1 carry the label “outlier”, declare all objects in C1 as outliers
◦ Any object that does not fall into the model for C (such as a) is considered an outlier as well
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Classification‐Based Method II: Semi‐Supervised Learning Cont’d
Comments on Classification‐based outlier detection methods:
Strength
• Outlier detection is efficient (fast)
Bottleneck
• Quality heavily depends on the availability and quality of the training set, but often difficult to obtain representative and high quality training data
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Summary
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Types of outliers ( Do you remember?)
Outlier detection (How about the detection methods?)
Statistical (or model‐based) approaches
Proximity‐base approaches
Clustering‐base approaches
Classification approaches
Mining contextual and collective outliers
Outlier detection in high dimensional data
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Agenda
• Outlier and Outlier Analysis
• Outlier Detection Methods
• Statistical Approaches
• Proximity‐Based Approaches
• Clustering‐Based Approaches
• Classification Approaches
• Mining Contextual and Collective Outliers
• Outlier Detection in High Dimensional Data
• Summary
• Discussions
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Discussions
•This “paper” is special, not a research paper  More of a survey for teaching purposes
• Open issues in Outlier and Anomaly Detection

The application of Intrusion Detection Systems
1) Short of some fundamental redesign, today’s outlier detection approaches in intrusion detection system will not be able to adequately protect tomorrow’s networks against intrusions and attacks;
2) Inability to suppress false alarms;
3) No globally acceptable standard/ metric for evaluating an intrusion detection system
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Questions?
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D. Agarwal. Detecting anomalies in cross‐classified streams: a bayesian approach. Knowl. Inf. Syst., 11:29–44, 2006.
F. Angiulli and C. Pizzuti. Outlier mining in large high‐dimensional data sets. TKDE, 2005.
C. C. Aggarwal and P. S. Yu. Outlier detection for high dimensional data. SIGMOD’01
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D. Dasgupta and N.S. Majumdar. Anomaly detection in multidimensional data using negative selection algorithm. In CEC’02
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References (II)
S. D. Bay and M. Schwabacher. Mining distance‐based outliers in near linear time with randomization and a simple pruning rule. KDD’03
D. Barbara, N. Wu, and S. Jajodia. Detecting novel network intrusion using bayesian estimators. SDM’01
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E. Eskin, A. Arnold, M. Prerau, L. Portnoy, and S. Stolfo. A geometric framework for unsupervised anomaly detection: Detecting intrusions in unlabeled data. In Proc. 2002 Int. Conf. of Data Mining for Security Applications, 2002.
E. Eskin. Anomaly detection over noisy data using learned probability distributions. ICML’00
T. Fawcett and F. Provost. Adaptive fraud detection. Data Mining and Knowledge Discovery, 1:291–316, 1997.
V. J. Hodge and J. Austin. A survey of outlier detection methdologies. Artif. Intell. Rev., 22:85–126, 2004.
D. M. Hawkins. Identification of Outliers. Chapman and Hall, London, 1980.
Z. He, X. Xu, and S. Deng. Discovering cluster‐based local outliers. Pattern Recogn. Lett., 24, June, 2003.
W. Jin, K. H. Tung, and J. Han. Mining top‐n local outliers in large databases. KDD’01
W. Jin, A. K. H. Tung, J. Han, and W. Wang. Ranking outliers using symmetric neighborhood relationship. PAKDD’06 E. Knorr and R. Ng. A unified notion of outliers: Properties and computation. KDD’97
E. Knorr and R. Ng. Algorithms for mining distance‐based outliers in large datasets. VLDB’98
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References (III)
E. M. Knorr, R. T. Ng, and V. Tucakov. Distance‐based outliers: Algorithms and applications. VLDB J., 8:237–
253, 2000.
H.‐P. Kriegel, M. Schubert, and A. Zimek. Angle‐based outlier detection in high‐dimensional data. KDD’08
M. Markou and S. Singh. Novelty detection: A review—part 1: Statistical approaches. Signal Process., 83:2481–2497, 2003.
M. Markou and S. Singh. Novelty detection: A review—part 2: Neural network based approaches. Signal Process., 83:2499–2521, 2003.
C. C. Noble and D. J. Cook. Graph‐based anomaly detection. KDD’03
S. Papadimitriou, H. Kitagawa, P. B. Gibbons, and C. Faloutsos. Loci: Fast outlier detection using the local correlation integral. ICDE’03
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References (IV)
A. Patcha and J.‐M. Park. An overview of anomaly detection techniques: Existing solutions and latest technological trends. Comput. Netw., 51, 2007.
X. Song, M. Wu, C. Jermaine, and S. Ranka. Conditional anomaly detection. IEEE Trans. on Knowl. and Data Eng., 19, 2007.
Y. Tao, X. Xiao, and S. Zhou. Mining distance‐based outliers from large databases in any metric space. KDD’06
N. Ye and Q. Chen. An anomaly detection technique based on a chi‐square statistic for detecting intrusions into information systems. Quality and Reliability Engineering International, 17:105–112, 2001.
B.‐K. Yi, N. Sidiropoulos, T. Johnson, H. V. Jagadish, C. Faloutsos, and A. Biliris. Online data mining for co‐
evolving time sequences. ICDE’00
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